Already known in the prior art is a three-way catalytic converter which can clean three major toxic components (HC, CO and NO.sub.X) in the exhaust gas. The operation of the three-way catalytic converter is effectively attained when the exhaust gas is in a state wherein excess air as well as excess fuel is not left in the exhaust gas, i.e., the air-fuel ratio of the exhaust gas (the ratio of air remaining in the exhaust gas to fuel remaining in the exhaust gas) is maintained near the stoichiometric value.
For maintaining the air-fuel ratio near the stoichiometric value, an air injection system has been provided in the prior art for controlling the amount of secondary air introduced into the exhaust manifold in accordance with electrical signals transmitted from an oxygen-concentration-cell type air-fuel sensor, for example, an O.sub.2 sensor which is arranged in an exhaust pipe of the engine. This air injection system has a vacuum-operated flow control valve including a spring-urged diaphragm which forms a vacuum chamber on one side thereof. To this chamber, a vacuum signal is selectively introduced from the intake manifold of the engine in accordance with the electrical signal transmitted from the O.sub.2 sensor. The amount of secondary air directed to the exhaust system is thus selectively increased for maintaining the air-fuel ratio of the exhaust gas directed to the catalytic converter near the stoichiometric value.
In the known air-injection system a relatively slow rate of increase in the amount of secondary air is maintained for effectively controlling the air-fuel ratio to the stoichiometric value during the constant rotational operation of the engine. However, this known system suffers from the drawback wherein the air-fuel ratio of the exhaust gas is not effectively controlled near the stoichiometric value when the engine begins to accelerate. The reason for this disadvantage is due to the operation of the acceleration pump during the time when the engine begins to accelerate for introducing an excess amount of fuel into the engine in order to produce a stabilized accelerating condition. The excess amount of fuel causes the air-fuel ratio in the exhaust pipe to reach a lean value which in turn prevents the catalytic converter from cleaning the NO.sub.X components remaining in the exhaust gas.